I recently inherited an iPhone 4, and I had no idea how to change its Apple password--necessary to install updates and acquire new applications. I stopped by to ask at the local Mac Store, and the young clerk assured me that it couldn't be done. That being the case, I thought I'd explain how simple it was to actually do. I'm doing this for people like myself who find a legitimate need to do this, but I'll also end with some suggestions to improve overall device security.
I'll begin with mentioning that the relative from whom I inherited this device left no password information, except a few cryptic security phrase notes in his wallet and a couple references to password reset when I searched the iPhone itself. He was a security expert, so I didn't have much hope in coming up with the correct password through trial and error.
When attempts to crack the password the traditional way were unsuccessful, I eventually received a message inquiring whether, or not, I wanted to reset the Apple password. I indicated that I did and, since his e-mail still resided on the device, I requested to reset the account using his e-mail. The e-mail arrived moments later, and I created the new password. That was indeed thankfully easy.
Bear in mind that the Apple password is not the same as the pass code or screen lock. Fortunately, this iPhone had no screen lock, or my job would have been much more difficult. On earlier iPhones, however, this can be broken by selecting emergency call from the lock screen, then navigating away. I don't know whether this particular vulnerability remains in the later models.
Should you wish to make your iPhone more secure, you may wish to consider requiring a screen pass code. In addition, I recommend registering your device through Aps such as Find iPhone.
If you have many electronic devices on which you've stored important family information and records, it's strongly recommended that you retain your passwords somewhere with the rest of your important papers. Should something happen to you, it makes the settling of your affairs a little simpler.
(By the way, changing the device name can easily by right-clicking on it within iTunes. I suggest also that you create a new Apple id, then sign-out of the old, and sign-into the new.)